Claudia Schillings (Warwick)
Analysis of the Ensemble Kalman Filter for Inverse Problems
The ideas from the Ensemble Kalman Filter introduced by Evensen in 1994 can be adapted to inverse problems by introducing artifical dynamics. In this talk, we
will discuss an analysis of the EnKF based on the continuous time scaling limits, which allows to derive estimates on the long-time behavior of the EnKF
and, hence, provides insights into the convergence properties of the algorithm. Results from various numerical experiments supporting the theoretical findings
will be presented.
Tony O'Hagan (Sheffield)
Inverting an Imperfect Model
As if inverse problems were not already hard enough, this talk will discuss an additional difficulty that has received relatively little attention - model discrepancy. All models are imperfect in practice, whether because they are actually wrong - wrong or incomplete physics - or because there are computational errors, and the difference between the model's predictions (using true or best parameter values) and reality is model discrepancy. How important this is depends on the purpose of inversion. If the goal is simply to tune the model to make predictions of new instances within the range of the calibration data - interpolation - then model discrepancy is relatively easy to address.
But if we wish to extrapolate to instances outside the context or range of the data, or if we actually wish to learn about the true physical values of model parameters, then model discrepancy is a fundamental problem and requires very careful attention.